Rasmussen's retort was the latest episode in what appears to be escalating tensions between the U.S. and Denmark. Trump said Tuesday that he was postponing his visit to the country in September in after Denmark's current prime minister, Mette Frederiksen, called his interest in purchasing Greenland "absurd."

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Trump a day later asserted that Denmark was not spending enough on NATO, tweeting, "For the record, Denmark is only at 1.35% of GDP for NATO spending."

"They are a wealthy country and should be at 2%," he argued. "We protect Europe and yet, only 8 of the 28 NATO countries are at the 2% mark. The United States is at a much, much higher level than that."

Rasmussen, who led the country from 2015 until June, responded by invoking the military commitment Denmark has made in Afghanistan.

And - as i told You at the NATO Summit in Bruxelles last year - we have had (proportionally) exactly the same numbers of casualties in Afghanistan as US. We always stands firm and ready - so we will not accept that our defence willingness is only about percentages.

"And — as i told You at the NATO Summit in Bruxelles last year — we have had (proportionally) exactly the same numbers of casualties in Afghanistan as US," he said on Twitter. "We always stands firm and ready — so we will not accept that our defence willingness is only about percentages."

The Danish Parliament in January added 1.5 billion kroner ($223 million) to its defense budget for 2023, according to The Associated Press. The budget will make defense spending 1.5 percent of gross domestic product (GDP) for the year.

The United States' defense spending, meanwhile, makes up about 3.4 percent of its GDP.

Trump and Denmark's relationship appears to have strained over Trump's expressed interest in purchasing Greenland, a semi-autonomous Danish territory. Trump told reporters on Sunday that he was interested in buying the island home to more than 50,000 people for strategic purposes.

Frederiksen denounced the idea as "absurd," prompting Trump to postpone his upcoming visit to the country in September.

"Denmark is a very special country with incredible people, but based on Prime Minister Mette Frederiksen’s comments, that she would have no interest in discussing the purchase of Greenland, I will be postponing our meeting scheduled in two weeks for another time," Trump tweeted on Tuesday.

On Wednesday, he called Frederiksen's remarks "nasty" and "inappropriate."

"All she had to say was say, ‘No, we wouldn’t be interested,'" Trump said.

Frederiksen said Wednesday that she does not believe the president's canceled trip will "influence on other matters" between the nations.